Guided Example #1 - Conditional Probability

At UCI, the probability that a student takes English and Statistics is 0.07. The probability that a student takes English is 0.8. What is the probability that a student takes Statistics given that the student is taking English?

A. $0.056$ B. $0.814$ C. $0.088$ D. None of the above

Step 1

We are given following events and their corresponding probabilities.
$P (English and Statistics) = 0.07$
$P (English) = 0.8$

Step 2

And we are asked to find P( Statistics given that the student is taking English)

Step 3

$P (Statistics | English) = \frac{P (Statistics and English)}{P (English)}$
$= \frac{P (Statistics ⋂ English)}{P (English)}$

Step 4

$= \frac{0.07}{0.8} = 0.0875 = 8.75 %$

All Steps

We are given following events and their corresponding probabilities.
$P (English and Statistics) = 0.07$
$P (English) = 0.8$

And we are asked to find P( Statistics given that the student is taking English)

$P (Statistics | English) = \frac{P (Statistics and English)}{P (English)}$
$= \frac{P (Statistics ⋂ English)}{P (English)}$

$= \frac{0.07}{0.8} = 0.0875 = 8.75 %$